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We consider the unit execution time unit communication time (UET-UCT) scheduling model with hierarchical communications [1], and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than 5/4 (unless 𝒫=𝒩𝒫). This result is an extension of the result of Hoogeveen et al. [6] who proved that there is no polynomial time ρ-approximation algorithm with ρ&lt;7/6 for the classical UET-UCT scheduling problem with homogeneous communication delays and an unrestricted number of identical machines.

TY - JOURAU - Bampis, EvripidisAU - Giroudeau, R.AU - König, J.-C.TI - On the hardness of approximating the UET-UCT scheduling problem with hierarchical communicationsJO - RAIRO - Operations Research - Recherche OpérationnellePY - 2002PB - EDP-SciencesVL - 36IS - 1SP - 21EP - 36AB - We consider the unit execution time unit communication time ($\!$UET-UCT$\!$) scheduling model with hierarchical communications [1], and we study the impact of the hierarchical communications hypothesis on the hardness of approximation. We prove that there is no polynomial time approximation algorithm with performance guarantee smaller than $5/4$ (unless ${\mathcal {P}}={\mathcal {NP}}$). This result is an extension of the result of Hoogeveen et al. [6] who proved that there is no polynomial time $\rho $-approximation algorithm with $\rho &lt; 7/6$ for the classical UET-UCT scheduling problem with homogeneous communication delays and an unrestricted number of identical machines.LA - engKW - scheduling; hierarchical communications; non-approximabilityUR - http://eudml.org/doc/245145ER -